Calculus · Week 32 · Applications of Integration
Average Value and Accumulation in Context
A definite integral can give an average value, a displacement, a total distance, or an amount in a tank, and pausing to ask which one is wanted keeps the work on track.
- Students will
- Students compute an average value, a displacement and total distance, and an accumulated amount, and state each answer with units.
- SEL skill
- Use a pause and check routine when displacement and total distance disagree
- What it looks like
- Students practice self-management by using a pause and check routine when displacement and total distance give different numbers.
- Content focus
- Average value, motion, and accumulation with integrals
- Format
- Data talk
Self-management
Self-management means noticing your stress and using a routine to stay focused, like pausing to check when two answers do not match. More self-management activities
What you get
A teacher guide with what to say, step by step, plus student pages and a supports page for students with diverse learning needs, including those with IEPs. Print or Project it, or assign it in Google Forms and Google Docs for Google Classroom. Your first 10 activities are free.
Standards
- AB 8.1: AP Calculus AB, Unit 8, Topic 8.1
- AB 8.2: AP Calculus AB, Unit 8, Topic 8.2
- AB 8.3: AP Calculus AB, Unit 8, Topic 8.3
- Standard for Mathematical Practice: MP6 Attend to precision
- CA Mathematics Framework (2023): Taking Wholes Apart, Putting Parts Together
- Traditional course: Calculus
More self-management activities for Calculus
- Getting Closer: Limits from Graphs and Tables Self-managementReading limits and one sided limits from tables and graphs, with a pause and check plan.
- Power Rule and Friends Self-managementFast derivative rules, with a pause and check routine that catches careless slips.
- The Chain Rule Self-managementTaking derivatives of functions inside functions, one layer at a time, without skipping steps.
- L'Hospital's Rule Self-managementPausing to check the form, then persisting when a limit first gives 0/0.
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